ETA: Heh! Immediately before hitting [Submit] on this magnum opus I scrolled to the bottom to see if @Richard_Pearse had already replied. Only to see him already having had the same thought. Who says pilots a) don’t think alike, and b) aren’t lazy? 
I got interrupted in the middle, so this was in-progress for longer than it appears. And it appears plenty long already. Sheesh! Anyhow, back to my planned post …
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@GrayGhost:
You think rightly.
Light twins are in a crappy spot during takeoff. Back when I owned a Twin Comanche based in Las Vegas, every takeoff involved passing through the no-man’s land where it will not fly on one engine. That’s pretty typical of any of the 4-7 person light twins, turbo-ed or otherwise. Every single takeoff except at sea level on a frigid day with a very light load transits no-man’s land. In that dangerous space any engine failure commits you to an unplanned landing that may be pretty violent and perhaps unsurvivable. But that’s still better than losing control and truly crashing in a flaming heap of crumpled metal.
I’ll use this aircraft type as a concrete example, but understand the big picture would be the same with any light or even medium twin; just the numbers & details would differ a smidgen.
Here’s a nice readable scan of the relevant Pilot Handbook.
From PDF page 38 = handbook page 2-2 we see that stall speed with flaps is 69, without flaps around 73, Vmca is 90, single engine climb is 105, and normal climb is 112. All in mph indicated airspeed. MPH was the standard for lightplanes back in the day; knots came later. The legal / engineering definitions of those speeds are given on PDF page 29 = handbook page 1-15.
All normally aspirated ICE engine takeoffs are made at full power. There ain’t no reserve. In the case of turbo-ed engines at low altitude airports there may be some more throttle travel left after settling the engine gauges onto the takeoff redlines, but pushing up the power into that beyond-redline range isn’t part of the plan and may blow the good engine apart right then and there.
Vmca is defined with one engine at full power and the other at failed windmilling = max drag. In other words, the most asymmetrical thrust possibility.
As you correctly surmise, from there if you could somehow add power on the good engine asymmetry would increase, controllability would get worse, and you’d need to be going faster to maintain control. Conversely if you reduce drag on the other side by feathering the dead propeller, asymmetry would decrease, controllability gets better and you could withstand being (a little) slower without losing control.
And here’s the punchline: by reducing power on the good engine, Vmca drops out of the picture. With one windmilling and the other reduced to half power or better yet to idle, you have plenty of control authority to handle that vastly reduced asymmetry even at and below stall speed. The good news is controllability becomes easy again. The bad news is with one quit and one (near-)idling, you’re slowing and descending quickly whether you like that or not.
Now to normal takeoffs. There’s a recap of speeds on PDF page 62 = handbook page 4-1. The takeoff itself is described on PDF page 67 = handbook page 4-7. Which says to (normally) leave flaps up, set full power on the engines, accelerate to Vr of 90 mph, then pull back to lift off. Retract the gear while accelerating in a very flat climb to 112, then climb at 112. It’s not a coincidence that the rotate speed is chosen to be Vmca.
Now what if something goes wrong? Which leads us to the takeoff engine failure procedure on PDF page 49 = handbook page 3-2.
If an engine hiccups significantly or quits:
If you haven’t hit 90 and lifted off yet, slam both throttles to idle, try to control the insane swerve you’re in the middle of, then once you’ve settled that down, apply wheel brakes as best you can (without anti-skid) to slow as best you can. There is no guarantee you can stop in the remaining pavement. If you’re going off the side or the end of the runway, aim for something soft and if you have the presence of mind, kill the engines and electrics before the crash occurs.
What if you have gotten above 90 and rotated and lifted off then the engine quits? 90 is Vmca; Yeager can fly the airplane at that speed on a good day, can you today? A soon as the engine hiccups even a smidgen, you’re going to be slowing towards 90. Starting from what, 92?, 95? Not a lot of headroom there.
Time to think fast. Level off, decide if you’re accelerating faster away from 90 or are doomed to losing speed slower towards 90. Also decide whether, even if you successfully accelerate, will you be able to clear whatever obstacles may be ahead? Remember you’re 10-20 feet above the ground and struggling like mad to keep going more or less straight while the airplane is trying very hard to turn hard right or left followed by going over on its back. You may already have involuntarily turned 20 degrees off the runway heading and be aimed at the hangars & offices lining the airport. At 20 feet above the runway, it doesn’t take much of a nearby building or tree or even parked airplane to be taller than you are.
If you’re slowing or don’t think you have room enough to climb enough, then slam both throttles to idle, remove all the asymmetric controls you just had input, and try to land/crash on the runway or at least on the softest / survivable-est thing you can find pretty much directly in front of you; there’s not time, space, nor speed to turn but a smidgen.
If you do think you can keep accelerating and missing obstacles, do that. Get up to 105 mph, then retract gear & flaps, feather the bad engine and start to climb at 105. Hope the general area around the airport is flat because you’ll be gaining ~100-300 feet vertically per mile of horizontal. At least for the first mile or two.
But even then, the recommendation throughout the 90-105 speed regime and even a little higher is that if a safe landing can still be made ahead, that’s smarter than trying to fly out of this predicament. Given a nice long airliner-sized runway, there’s probably enough runway left to do this without scraping the paint. Slam both throttles to idle, land on the pavement ahead, and try to stop. Even if the runway isn’t so generous, crashing at 30 mph upright while traveling only horizontally is far more survivable than crashing at 90 or 110 mph perhaps upside down and perhaps with a lot of vertical speed too.
Even if you pass through the 90-105 no man’s land with no failures and get established in the normal climb at 112 and get the gear & flaps up, you’re still in a ticklish spot. If an engine quits you can lose that 22 mph back to 90 real quickly. Any more than 7 mph of speed loss you’re below the 105 value and now you’re not climbing optimally and will need to flatten out even more to regain that speed. Hope there’s no hills or tall buildings or antenna towers nearby.
Meanwhile it’ll still be a handful of trying to turn / roll over though not as bad as it would be back at 95ish. Of course about then you’re normally talking on the radios, turning out of traffic, perhaps entering the clouds. If an engine quits here you’ve got a huge head start being clean and fast(er), but this thing can still go from normal to a desperate fight for survival in about 4 seconds flat. If you’d put the engine failure “script / decision tree” out of mind once you got settled in climb, you may not get it back in the time available.
Startle is the technical term for when stuff you really didn’t anticipate happened anyhow. It’s the bolt from the blue surprise and humans go stupid for a few seconds when it happens. Piloting is all about becoming as startle-resistant as possible by actively anticipating the particular applicable worst-case bad event(s) all day every day. Remaining consciously primed to deal with an engine failure for the first few minutes of the flight, not just the first few seconds, is an example of startle-proofing. Later in the flight other emergencies become the largest snake. For us enroute it’s rapid depressurization first & engine failures second. With collision and wake turbulence risks being the biggees during climb & descent.
Effective takeoff failure training in a light twin is difficult precisely because the maneuver is such a knife edge with an exponential feedback loop at the bitter end. And perforce must be practiced near the ground. Lots of people killed themselves in the 1960s learning how close we can come to tickling that dragon. We need to get close enough to learn sorta how it looks and feels, but not so close that the slightest imperfection in performance is fatal. So pilots, even diligent well-trained ones, never have the chance to know the true edge of the precipice. Sure, you can and do fly Vmca demos at altitude. But that garter snake is a pale cousin of the cobra that lives down near the ground.
The real challenge is mental. Before adding power, you have to say to yourself: “I am fully willing to deliberately crash this X-hundred thousand dollar airplane during this takeoff as the least bad way to probably survive.” Folks who don’t go through that litany are the ones who (often unwittingly) choose to violate the invisible barrier at Vmca rather than taking the visibly scary choice of a forced/crashed landing off the runway.
The difference is the Vmca violators die inverted in a mass of burning fuel & crumpled aluminum every time. The forced landers usually walk away or are carried out by the EMTs. The airplane is often a write-off, but that’s what insurance is for.
That’s enough of a book for tonight; time for dinner here.